In this paper, we show that one of the most widely used methods to solve the non-linear viscous-plastic (VP) sea ice rheology, the elastic-viscous-plastic (EVP) method, generates artificial linear bands of high deformation that may be confounded with real linear kinematic features observed in the Arctic ice pack. These numerical artefacts are easily filtered out by using a slightly different regularization of the internal stress. In addition, the EVP method is reinterpreted as an iterative solver and a clear distinction appears between the numerical and physical parameters. Two numerical parameters determine the stability and accuracy of the method and are adjusted to avoid the noisy ice deformation fields frequently observed with the EVP method in nearly rigid ice areas. This study also confirms the unsatisfactory numerical convergence of the EVP method and investigates the effects of the numerical parameters on sea ice deformation, internal stress and velocity fields obtained with unconverged solutions.